The obvious part, the name "Game" comes directly from the Neil Strauss book: The game. Which is a 100% PUA book. Similar to how terms like "looksmaxxing" entered mainstrem through incels, "Game" entered mainstream by dilluting PUA concepts. The dillution was removing the most nonsensical and mysogynistic tactics like bringing blacklights to dates so you can make elaborate insults to women's clothing (yeah this is real) to pseudoscientific "millenary" (with a millenary history of failure) techniques like

Play hard to get, be assertive, be dominant

Or vague nonsense like

Be the best version of yourself

And the reason why many man belive this comes from three traits that come from gambling

1-Gambling near miss: These guys will spend hours practicing their "psychological tricks" and "social skills" to talk to girls, entertain them for 10 minutes and get rejected. They see this as "improvement" or "i almost got it", not different from the gambler that almost got the jackpot, this near miss motivates the gambler to keep gambling, because he must be doing something right, yet his success is still controlled by random chance.

2- Follow the winner: They observe guys that get multiple girls by having "game" and it keeps them hooked in their gamble, they see themselves as just lacking practice and experience, and by honing their skills, they can be just as good as the succesful guy, which again, fails to consider correlation-causation and isolation of different factors, including luck.

3- Jackpot euphoria: For someone that has nothing, getting a girls number after hitting on 50 girls is enough evidence that his efforts are working. They are not really interested in assessing the cause or be bothered by the very low success rate they have. They never ask this question to themselves: If i hopped on tinder with a nice picture and simply asked girls "Hey, wanna have sex?" and see the success rate to compare and really understand if its worth it investing your precious time to entertain other people. Its hard for them to simply think that "Well, the girl just liked me, there was no "skill" or "seduction", just compatibility"

These things fail most of the time, and the one of the biggest evidence for that is that there was a direct pipeline between PUA community and incel community, which is what created the term "Puahate". Loads of men spend days of their life practicing pseudoscience, the vast majority of them fail, they get mad and rebel against their master.

This is just a result of male's inherent more competitive sexual nature. Men and women dislike rejection, but women often don't cope, men are hardwired to try and find numerous explanations and alternative solutions to the fact that they don't get pussy

Moreover, women often only approach who they want. Men that are unsuccesful with dates will eventually approach any woman, and after they get rejected by any woman, there is a big hit to their ego and self steem: You have no sexual or dating value. And this is so crushing that it explains why incels like self deprecation and dwelling on their own failures so much

So, its a pipeline, men that are not sexually appealing go from

PUA/Game-->RP/MGTOW-->Incel

And since people lack more and more social interaction, this only gets worse.

Despite being ridden with woman-hating practices, all of these are still in the end seeking woman's approval. Even the ones that say "i'm done with dating" still want to be able to pump and dump, they still want to be sexually valuable to women.

Its not going to change until men find a way to remove sexual validation as a necessary part of their life. And, to be honest, culture does not help with this at all, only reinforces.